On the growth and dissemination laws in a mathematical model of metastatic growth

TL;DR

This paper develops and tests a mathematical model of metastatic cancer growth focusing on dissemination and colonization, revealing limitations in data to distinguish between different growth assumptions.

Contribution

It formalizes metastatic growth into simple laws and analyzes the identifiability of model parameters using experimental data.

Findings

Two growth assumptions fit data equally well

Dissemination law's fractal dimension coefficient is not uniquely identifiable

Data limitations restrict inference of detailed metastatic growth parameters

Abstract

Metastasis represents one of the main clinical challenge in cancer treatment since it is associated with the majority of deaths. Recent technological advances allow quantification of the dynamics of the process by means of noninvasive techniques such as longitudinal tracking of bioluminescent cells. The metastatic process was simplified here into two essential components -- dissemination and colonization -- which were mathematically formalized in terms of simple quantitative laws. The resulting mathematical model was confronted to in vivo experimental data of spontaneous metastasis after primary tumor resection. We discuss how much information can be inferred from confrontation of theories to the data with emphasis on identifiability issues. It is shown that two mutually exclusive assumptions for the secondary growth law (namely same or different from the primary tumor growth law) could fit equally well the data. Similarly, the fractal dimension coefficient in the dissemination law could not be uniquely determined from data on total metastatic burden only. Together, these results delimitate the range of information that can be recovered from fitting data of metastatic growth to already simplified mathematical models.